Solve for $b$. $7b-\dfrac25=6b-\dfrac75$ $b=$
Solution: We need to manipulate the equation to get $ b $ by itself. $\begin{aligned} 7b-\dfrac25&=6b-\dfrac75 \\\\ 7b-\dfrac25 {-6b} &= 6b-\dfrac75{-6b} &&\gray{\text{Subtract 6b from each side.}}\\\\ 1b-\dfrac25&=-\dfrac75 &&\gray{\text{Combine like terms.}}\\\\ 1b-\dfrac25{+\dfrac25} &= -\dfrac75{+\dfrac25} &&\gray{\text{Add }\dfrac25\text{ to each side.}}\\\\ 1b &=-1 &&\gray{\text{Combine like terms.}}\\\\ \dfrac{1b}{{1}} &= \dfrac{-1}{{1}} &&\gray{\text{Divide each side by 1}}\\\\ b &= {-1} &&\gray{\text{Simplify.}}\\\\ \end{aligned}$ The answer: $b = { -1 }~~~~~~~~$ [Let's check our work!]